A new proof for the convergence of Picard's filter using partial Malliavin calculus

Hideyuki Tanaka

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arXiv · 1311.6090

A new proof for the convergence of Picard's filter using partial Malliavin calculus

Hideyuki Tanaka

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Abstract

The discrete-time approximation for nonlinear filtering problems is related to both of strong and weak approximations of stochastic differential equations. In this paper, we propose a new method of proof for the convergence of approximate nonlinear filter analyzed by Jean Picard (1984), and show a more general result than the original one. For the proof, we develop an analysis of Hilbert space valued functionals on Wiener space.

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Hideyuki Tanaka. 2014-05-23. A new proof for the convergence of Picard's filter using partial Malliavin calculus. https://arxiv.org/abs/1311.6090

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